Trigonometry Quizzes: Test Your Understanding of Trig Functions

Question 1

Determine the amplitude of the function h(x) = 3sin(x - π/3).

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 2

Calculate the area of a triangle with sides a, b, and c, where the angle between sides a and b is θ.

Accepted Answer

absin(θ)/2

Answer

abcos(θ)/2

Answer

bcsin(θ)/2

Answer

accos(θ)/2

Question 3

Which of the following is equivalent to sin(π/3) + cos(π/3)?

Accepted Answer

√3/2

Answer

1

Answer

√2/2

Answer

2

Question 4

The height of a building is 100 feet. From a distance of 300 feet away, what is the angle of elevation to the top of the building?

Accepted Answer

36.87°

Answer

18.43°

Answer

45°

Answer

73.74°

Question 5

In a triangle with sides a, b, and c, which formula represents the sine rule?

Accepted Answer

a/sin(A) = b/sin(B) = c/sin(C)

Answer

a/cos(A) = b/cos(B) = c/cos(C)

Answer

a/tan(A) = b/tan(B) = c/tan(C)

Answer

a/cot(A) = b/cot(B) = c/cot(C)

Question 6

What is the inverse function of the cosine function?

Accepted Answer

Arccosine

Answer

Sine

Answer

Cosine

Answer

Tangent

Question 7

Determine the equation of the tangent function with a period of π.

Accepted Answer

f(x) = tan(x/2)

Answer

f(x) = tan(x)

Answer

f(x) = tan(2x)

Answer

f(x) = tan(x/4)

Question 8

What is the amplitude of the function y = 2cos(3x)?

Accepted Answer

2

Answer

1

Answer

3

Answer

6

Question 9

If the measure of an angle is θ and tanθ = √3, what is the value of sinθ?

Accepted Answer

√3/2

Answer

1/2

Answer

1

Answer

2

Question 10

Which of the following is the inverse function of tanx?

Accepted Answer

arctanx

Answer

arccosx

Answer

arcsinx

Answer

arccotx

Question 11

What is the domain of the function y = cotx?

Accepted Answer

{x | x ≠ π/2 + nπ, n ∈ Z}

Answer

{x | x ≠ nπ, n ∈ Z}

Answer

{x | x ≠ 0}

Answer

{x | x ≠ 1}

Question 12

Which of the following is a theorem that relates the sides and angles of a right triangle?

Accepted Answer

Pythagorean theorem

Answer

Sine theorem

Answer

Cosine theorem

Answer

Tangent theorem

Question 13

In a right triangle, the ratio of the length of the opposite side to the length of the hypotenuse is called the:

Accepted Answer

sine

Answer

cosine

Answer

tangent

Answer

cotangent

Question 14

What is the value of tan(45 degrees)?

Accepted Answer

1

Answer

0

Answer

-1

Answer

undefined

Question 15

What is the amplitude of the function y = 3 cos(4x)?

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 16

What is the domain of the function y = cot(x)?

Accepted Answer

{x | x ≠ (2n + 1)π/2}

Answer

All real numbers

Answer

{x | x ≠ nπ}

Answer

{x | x ≠ π/2}

Question 17

In a right triangle with sides a, b, and hypotenuse c, which of the following is equal to the ratio of the length of the opposite side to the length of the hypotenuse?

Accepted Answer

The sine of the angle opposite side a

Answer

The cosine of the angle opposite side b

Answer

The tangent of the angle opposite side a

Answer

The cotangent of the angle opposite side b

Question 18

What is the domain of the trigonometric function y = tan(x)?

Accepted Answer

{x | x ≠ (π/2) + kπ, k ∈ ℤ}

Answer

All real numbers

Answer

{x | x ≠ 0, x ≠ π/2, x ≠ π, ...}

Answer

{x | x ≠ kπ, k ∈ ℤ}

Question 19

Prove the trigonometric identity: sin(2x) = 2sin(x)cos(x).

Accepted Answer

Use the double-angle formula: sin(2x) = 2sin(x)cos(x).

Answer

Use the sum-to-product formula: sin(2x) = sin(x + x) = sin(x)cos(x) + cos(x)sin(x).

Answer

Use the Pythagorean identity: sin(2x) = (sin(x) + cos(x))^2.

Answer

Use the half-angle formula: sin(2x) = sqrt((1 + cos(2x)) / 2).

Question 20

In a right triangle, the ratio of the length of the side opposite the right angle to the length of the hypotenuse is known as the:

Accepted Answer

Sine

Answer

Secant

Answer

Tangent

Answer

Cosine

Question 21

Which trigonometric identity can be used to express the cosine ratio in terms of the sine ratio?

Accepted Answer

cos²θ = 1 - sin²θ

Answer

sin²θ + cos²θ = 1

Answer

cot²θ - 1 = csc²θ

Answer

tan²θ + 1 = sec²θ

Question 22

What is the period of the function y = sin(x)?

Accepted Answer

2π

Answer

π/2

Answer

π

Answer

4π

Question 23

What is the range of the cosine function?

Accepted Answer

[-1, 1]

Answer

The set of all acute angles

Answer

The set of all angles

Answer

The set of all positive numbers

Question 24

Which trigonometric identity gives the reciprocal of the sine function?

Accepted Answer

cscθ = 1/sinθ

Answer

cotθ = 1/tanθ

Answer

secθ = 1/cosθ

Answer

sinθ = 1/cscθ

Question 25

In a right triangle, what is the name of the side opposite the right angle?

Accepted Answer

Opposite side

Answer

Adjacent side

Answer

Base

Answer

Hypotenuse

Question 26

Which of the following trigonometric identities is always true?

Accepted Answer

sin² θ + cos² θ = 1

Answer

sin θ + cos θ = 1

Answer

cot θ = cos θ / sin θ

Answer

tan θ = sin θ / cos θ

Question 27

The trigonometric function f(x) = sin(x) is considered:

Accepted Answer

Periodic

Answer

Monotonic

Answer

Odd

Answer

Even

Question 28

Which of the following is NOT a Pythagorean Triple?

Accepted Answer

(3, 4, 7)

Answer

(7, 24, 25)

Answer

(8, 15, 17)

Answer

(5, 12, 13)

Question 29

The area of a triangle with sides of length a, b, and c can be calculated using:

Accepted Answer

Heron's formula

Answer

The Pythagorean Theorem

Answer

The Law of Sines

Answer

The Angle Bisector Theorem

Question 30

Which of the following is a practical application of trigonometry in the real world?

Accepted Answer

Navigation

Answer

Algebra

Answer

Geometry

Answer

Physics

Question 31

In a right triangle, the ratio of the length of the adjacent side to the length of the hypotenuse is known as:

Accepted Answer

Cosine

Answer

Tangent

Answer

Cosecant

Answer

Sine

Question 32

Which trigonometric identity states that sin²θ + cos²θ = 1?

Accepted Answer

Pythagorean identity

Answer

Double-angle identity

Answer

Sum-to-product identity

Answer

Half-angle identity

Question 33

What is the period of the cosine function?

Accepted Answer

2π

Answer

π

Answer

4π

Answer

∞

Question 34

What is the amplitude of the sine function f(x) = 4sin(x)?

Accepted Answer

4

Answer

1

Answer

2

Answer

8

Question 35

Which of the following is an example of a real-life application of trigonometry?

Accepted Answer

Surveying

Answer

Biology

Answer

Philosophy

Answer

Accounting

Question 36

What is the range of values for the cosine function?

Accepted Answer

[-1, 1]

Answer

[0, 1]

Answer

(-1, 1)

Question 37

For which angle is the tangent function undefined?

Accepted Answer

90°

Answer

30°

Answer

60°

Answer

45°

Question 38

In a right triangle ABC, where AB is the hypotenuse and BC is the side opposite angle A, what is the sine of angle A?

Accepted Answer

BC/AB

Answer

AB/BC

Answer

AC/AB

Answer

AB/AC

Question 39

What is the period of the trigonometric function y = sin(x)?

Accepted Answer

2π

Answer

π/2

Answer

4π

Answer

π

Question 40

From a point 20 feet away from the base of a tree, the angle of elevation to the top of the tree is 45 degrees. What is the height of the tree?

Accepted Answer

20 feet

Answer

10 feet

Answer

28.28 feet

Question 41

If tan(θ) = 1, what are the possible values of θ in the interval 0° ≤ θ ≤ 360°?

Accepted Answer

45° and 225°

Answer

45° only

Answer

90° and 270°

Answer

225° only

Question 42

What is the amplitude of the trigonometric function y = 2cos(x)?

Accepted Answer

2

Answer

2π

Answer

π

Answer

1

Question 43

Which of the following is equivalent to cos(90° - θ)?

Accepted Answer

sin(θ)

Answer

-sin(θ)

Answer

cos(θ)

Answer

-cos(θ)

Question 44

A right triangle has a hypotenuse of 10 cm. If one interior angle measures 30 degrees, what is the length of the opposite side?

Accepted Answer

5 cm

Answer

5√3 cm

Answer

10 cm

Answer

10√3 cm

Question 45

What is the value of sin(60°)?

Accepted Answer

√3/2

Answer

√2/2

Answer

1/2

Answer

1

Question 46

A 12-foot ladder leans against a vertical wall, forming an angle of 60 degrees with the ground. How high up the wall does the top of the ladder reach?

Accepted Answer

6√3 feet

Answer

12√3 feet

Answer

6 feet

Answer

12 feet

Question 47

Which trigonometric identity is true?

Accepted Answer

tan²θ + 1 = sec²θ

Answer

sin²θ + cos²θ = 1

Answer

csc²θ - cot²θ = 1

Answer

sec²θ - tan²θ = 1

Question 48

What is the period of the function y = sin(2x)?

Accepted Answer

π

Answer

2π

Answer

4π

Answer

π/2

Question 49

A surveyor measures the angle of elevation to the top of a building to be 25 degrees while standing 100 feet from its base. How tall is the building?

Accepted Answer

100 tan(25°) feet

Answer

100 sin(25°) feet

Answer

100 cos(25°) feet

Answer

100/tan(25°) feet

Question 50

What is the amplitude of the function y = 3 cos(x)?

Accepted Answer

3

Answer

π

Answer

2π

Answer

1

Question 51

If cos(θ) = 1/2, what is the value of sin(θ)?

Accepted Answer

√3/2

Answer

1/2

Answer

-1/2

Answer

-√3/2

Question 52

A circle has a radius of 5 cm. What is the length of an arc subtended by an angle of 60 degrees?

Accepted Answer

5π/3 cm

Answer

5π cm

Answer

π/3 cm

Answer

10π/3 cm

Question 53

Which of the following is NOT a quadrantal angle?

Accepted Answer

30°

Answer

180°

Answer

90°

Answer

270°